Stability of Composite Plates with a Dense System of Ribs in Two Directions

Area of Science:

• Mechanical Engineering
• Materials Science
• Solid Mechanics

Background:

• Composite plates with periodic microstructures present challenges due to oscillating coefficients in governing equations.
• Existing analytical solutions are complex and computationally intensive.

Purpose of the Study:

• To develop an easy-to-use analytical method for stability analysis of composite plates.
• To simplify the analysis of complex composite structures.
• To compare the proposed method with existing numerical techniques like FEM.

Main Methods:

• Transformation of governing partial differential equations using tolerance averaging.
• Obtaining a system of partial differential equations with constant coefficients.
• Analytical solution of the simplified equations.

Main Results:

• The simplified equations resemble classic equations for homogeneous plates, enabling straightforward analytical solutions.
• The proposed method requires substantially fewer computational resources than FEM analysis.
• Comparative analysis with FEM validates the accuracy of the new method.

Conclusions:

• The developed analytical method is efficient and accurate for stability analysis of composite plates.
• The method is suitable for engineering applications due to its simplicity and low computational cost.
• The study analyzed the influence of microstructure on critical forces.